A popular method for multivariate non-Gaussian data is probabilistic FPCA
[1]}, based on likelihood optimization.
For the case of Gaussian functional data,
[2]} and [3]} use a similar approach
based on mixed-effects regression.
[4]} adapted these methods in a paired-curve setting.
[5]} extended the ideas of [2]} and [4]}
to non-Gaussian functional data and combined them with a clustering approach.
Recently, [8]} further adapted the mixed model-based approach
by introducing a link function and estimating the GFPCA based on computationally efficient
variational approximations.
To the best of our knowledge, efficient approximations are available only for Gaussian and binary data
and are not directly adaptable to further exponential family distributions.
